Increasing iteration semigroups of Jensen set-valued functions

Abstract

Let S be a closed convex cone with non-empty interior in a real separable Banach space and cc(S) denote the set of all non-empty convex compact subsets of S. A necessary and sufficient condition is given under which a family {f ^t : t > 0} of set-valued functions f ^t : S → cc(S) is an increasing iteration semigroup of continuous Jensen set-valued functions.